Highest Common Factor of 471, 654, 709 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 471, 654, 709 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 471, 654, 709 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 471, 654, 709 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 471, 654, 709 is 1.
HCF(471, 654, 709) = 1
HCF of 471, 654, 709 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 471, 654, 709 is 1.
Highest Common Factor of 471,654,709 is 1
Step 1: Since 654 > 471, we apply the division lemma to 654 and 471, to get
654 = 471 x 1 + 183
Step 2: Since the reminder 471 ≠ 0, we apply division lemma to 183 and 471, to get
471 = 183 x 2 + 105
Step 3: We consider the new divisor 183 and the new remainder 105, and apply the division lemma to get
183 = 105 x 1 + 78
We consider the new divisor 105 and the new remainder 78,and apply the division lemma to get
105 = 78 x 1 + 27
We consider the new divisor 78 and the new remainder 27,and apply the division lemma to get
78 = 27 x 2 + 24
We consider the new divisor 27 and the new remainder 24,and apply the division lemma to get
27 = 24 x 1 + 3
We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 471 and 654 is 3
Notice that 3 = HCF(24,3) = HCF(27,24) = HCF(78,27) = HCF(105,78) = HCF(183,105) = HCF(471,183) = HCF(654,471) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 709 > 3, we apply the division lemma to 709 and 3, to get
709 = 3 x 236 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 709 is 1
Notice that 1 = HCF(3,1) = HCF(709,3) .
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Frequently Asked Questions on HCF of 471, 654, 709 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 471, 654, 709?
Answer: HCF of 471, 654, 709 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 471, 654, 709 using Euclid's Algorithm?
Answer: For arbitrary numbers 471, 654, 709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
